Results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion, which is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype.
Abstract
KV-cache compression is often justified by attention maps with a few large weights. This is incomplete: large weights may not contain most of the mass, omitted values can cancel, and preserving the attention output may not preserve the task. We separate these questions. Global score gaps -- not threshold counts -- determine how many tokens are needed to retain a target mass. For a realized row, the weighted sum of omitted values is the exact missing statistic. A controlled retrieval--aggregation model explains when truncation helps and when it hurts. These results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion. Under matched budgets, CertKV is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype. Compressibility depends on the mass, values, future queries, and task -- not on a sparse-looking map alone.
Long-context inference in large language models (LLMs) is increasingly limited by the memory required for the key-value (KV) cache. KV cache compression addresses this problem by reducing the storage cost of previous tokens. Among existing approaches, low-rank compression is particularly attractive because it represents every token in reduced dimensions. Previous low-rank methods typically derive fixed projection spaces from model weights, construct fixed spaces from calibration activations, or construct a shared basis over a broad cache region. Such representations may not capture detailed but important information. We partition each per-head KV cache into fixed-length logical pages and observe substantial low-rank structure within individual pages. Based on this observation, we propose PuzzleKV, a training- and calibration-free method that treats each completed page as an independent compression unit. PuzzleKV decomposes pages within each layer and KV head, computes attention directly over dense and factorized pages, and incrementally compresses newly eligible pages during autoregressive decoding. Experiments across models, context lengths, and benchmarks demonstrate the effectiveness of PuzzleKV under matched storage budgets. At approximately 60% of the original KV cache storage, PuzzleKV achieves more than 96% of Full KV performance across both evaluated models and all benchmark settings, with substantial gains over Global SVD on RULER and competitive performance on LongBench. To achieve a more aggressive compression ratio, PuzzleKV can be further combined with quantization while retaining more than 93% of Full KV performance using only 18.7% of the original storage.
Zizhong Wang, Jieying Wang, Zhao Zhang et al.· 0 citations
The key-value (KV) cache is the main memory bottleneck in long-context large language model (LLM) inference. Two leading training-free families are both structurally limited: token-selection methods (SnapKV, Ada-KV) score importance from an observation window and evict low-scoring tokens, but eviction is irreversible -- so when the importance signal degrades under query-agnostic reuse, accuracy collapses by 11-15 points; uniform low-rank coding keeps every token but spends equal rank everywhere, wasting budget. We observe that both failures share one cure: rank should be allocated, not evicted. We present VarRate, a training-free KV codec that assigns each token a variable low-rank budget by its query salience, keeping every token at a nonzero rank. Comparable adaptive-rank codecs reach this allocation only through training; VarRate requires none. Because no token is dropped, it degrades by only 3.5-5.5 points where query-aware selection collapses. At a matched 20% budget on LongBench (16 tasks), VarRate stays within 0.8 points of the uncompressed model on both Llama-3.1-8B and Qwen2.5-7B. Averaged over the two, it is the strongest matched-memory compressor. It significantly beats its uniform-rank ablation on both models. Against KVzip, a method purpose-built for query-agnostic reuse, it is accuracy-equivalent in three of four settings and within a point overall, at about one-eighth the prefill overhead.
Shahrzad Esmat, Dhawal Shah, Ali Jannesari· arXiv.org· 0 citations
ContourKV, a training-free allocator built from the dropped-mass statistic, wins $93$ of $160$ paired comparisons against that state of the art and loses $22$ at the byte count of the budget-enforcing baselines, and it ties the strongest of them.
Top-$K$ sparse attention reduces the cost of Softmax and value aggregation by attending to only a small subset of key--value (KV) entries. However, identifying this subset still requires scoring the current query against the full KV cache and performing global Top-$K$ selection, leaving selector cost linear in context length and limiting the practical efficiency of sparse attention for long-context decoding. In this paper, we introduce ReTopK, a training-free method that accelerates dynamic Top-$K$ attention by reusing historical retrieval decisions. ReTopK builds on the observation that similar queries often attend to overlapping supports and that partially overlapping supports can still preserve most of the Exact Top-$K$ attention mass. For each attention head, it maintains a bounded cache of historical query--support pairs, retrieves the most similar cached queries for each new query, unions their stored supports with a recent window, and reranks only the resulting compact candidate set using exact current-query scores. A similarity-based fallback invokes full-history Exact Top-$K$ when reuse is unreliable, while periodic exact refreshes limit cache drift. ReTopK retains the complete KV cache and reuses only selected indices, rather than historical scores, attention weights, or outputs. Across 16K--128K contexts, ReTopK achieves the lowest PG19 perplexity and the highest NIAH and LongBench scores among the evaluated approximate methods. At 128K with $K=512$, ReTopK incurs only a 0.50\% perplexity increase over Exact Top-$K$ while accelerating attention computation by $3.07\times$.
Sparse attention bounds downstream attention work by retaining a fixed-size subset of indexed tokens, but its standalone exact Top-$K$ stage must still process materialized score rows whose length grows with context. Production radix selectors discover their first actionable boundary only after a complete-row pass, forcing another row-scale traversal before exact refinement. We observe that locating a compact upper tail requires substantially less resolution than identifying the exact rank boundary, and that fixed-stride partial views of the current row remain calibrated to the corresponding complete-row rank across ragged lengths. We present HPC-Ops Top-K, a sample-guided exact selector for ragged sparse-attention score rows. A fixed-stride view proposes a row-local coarse boundary; the mandatory complete-row pass certifies its sufficiency, forms the admitted candidate set, and initializes exact FP32 refinement over the unresolved frontier. A nested secondary boundary and exact recovery handle underfilled proposals before any output is committed, so sampling controls common-path work but never correctness. The GPU implementation fuses complete-row certification and candidate formation, and combines persistent, KV-split, and direct-exact execution behind graph-capturable ragged-row dispatch. We evaluate HPC-Ops Top-K on indexer scores from Hy4-Preview. It outperforms the fastest verified external exact baseline by $1.29$--$1.75\times$ across 20 operator configurations, with a $1.55\times$ geometric-mean speedup. It further achieves $1.36\times$ and $1.48\times$ speedups on two framework-derived sparse-attention traces. The implementation is available in HPC-Ops, Tencent's open-source high-performance operator library for LLM inference, at https://github.com/Tencent/hpc-ops.
Data-adaptive sparse attention masks substantially outperform fixed patterns (e.g., BigBird and Longformer) and can even exceed dense attention on long sequences. Existing adaptive approaches---including SBM-Transformer, Dynamic Mask Attention, and NSA---typically require additional learnable parameters, custom gradient estimators, or specialized CUDA kernels. We show that classical data compression provides an effective masking signal with \textbf{no additional parameters}. By computing per-block gzip compression ratios, we identify non-redundant content blocks and route long-range attention selectively through them. Intuitively, blocks that gzip cannot compress contain information not predictable from local repetition, making them natural long-range attention targets. Because the compression profile is input-dependent, the resulting sparse mask adapts dynamically to content without learned parameters, auxiliary losses, or custom kernels. On PG-19 byte-level language modeling at 92M parameters with 8K context, our method achieves 1.71 bits-per-byte (BPB), outperforming dense attention (2.89), BigBird (2.34), Longformer (3.21), and a reimplemented SBM-Transformer (3.38)---the only learned-mask baseline---by up to 1.67 BPB while adding no parameters. The advantage grows with sequence length, with the gap over BigBird widening from 0.05 BPB at 4K context to 0.63 BPB at 8K, while convergence is 3.3$\times$ faster.
